Does battery tender charge hybrid battery?

No. It can't. When you shutdown the system, that 12-volt battery is used to disconnect the battery-pack. (It flips a relay.)

If you truly want to know state-of-charge level, you'll need to use an aftermarket app. The dashboard display is only a generalized depiction.

 

what is the hybrid battery level when you shut down at the end of the day?

 

Changes in temperature will also change the amount of charge the hybrid battery has and can hold. Since spring is rolling in, the battery will start to be able to hold more charge than the winter.

 

I once a couple times a year charge my 12v battery and it always seems I get better MPG after doing so. No scientific reasoning here, just my personal judgement.

FYI: I always personally try to charge my battery to 80%, or at least 50% if leaving it overnight or a few days. For me its not too difficult, just keep the car from using the hybrid battery to cruise down my street and then slow down to charge it before pulling into the driveway.

 

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If I understand the hybrid system explanation by The Car Care Nut and others on YouTube (for what that’s worth) there is no physical connection between the two when everything is shut down, so it shouldn’t be possible. Plus, considering the size of the traction battery, the battery tender isn’t capable of charging it to that level overnight unless it putting out a lot more amps than I understand them capable of at the tender setting.